An officer is always late to the office and arrives within the grace period of ten minutes after the start. Let X b the time that elapses between the start and the time the officer signs in with a probability density function.
$$f(x)=\begin{cases} kx^2&:& 0\leqslant x\leqslant 10\\0 &:& \text{otherwise}\end{cases}$$
where k > 0 is a constant.
Compute the value of K.
Find the probability that the he arrives less than 3 minutes after the start of the office.
Straightforward enough. $1 = k\int_0^{10}x^2dx$. You should be able to solve for k knowing this. The second part is the value of $k\int_0^{3}x^2dx$ using $k$ from the first part.